Inference with the lognormal distribution
N.T. Longford
Abstract
Several estimators of the expectation, median and mode
of the lognormal distribution are derived.
They have the form $\exp(\hmu+b\hsi^2)$,
where $\hmu$ and $\hsi^2$ are the usual estimators
of the mean and variance of the underlying normal distribution,
and $b$ is a suitable constant or function of $\hsi^2$.
The estimators aim to be approximately unbiased, efficient,
or to have a minimax property in the class of estimators we consider.
The small-sample properties of these estimators are assessed
by simulations and, when possible, analytically.
Some of these estimators of the expectation are far more efficient
than the maximum likelihood or the minimum-variance unbiased estimator,
even for substantial sample sizes.
In Journal of Statistical Planning and Inference 139, 2009.